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When do you want to pay the taxes on your money, now or when you take it out? Will reducing your taxable income now be really beneficial to you? You need to answer those questions for yourself. Roth can be a really good option if you can afford today's taxes because the growth is tax free and the disbursements are tax free. That is powerful in retirement planning.

Pre tax can be helpful because you are saving a percentage before the taxes hit, so you might save a little more and it reduces your taxable income, you might owe the feds less money on tax day. When you go to take the disbursement you have to pay federal income taxes on it.

In both scenarios, the maximum you can save without paying a 6% tax is $6,500 a year if you are under 50. That is the benefit of a 401(k) plan, your maximum contribution is $22,500, also your employer match doesn't count against that limit.

EDIT - I interpreted ROTH as a Roth IRA, not a Roth 401(k). In general, though, the same considerations are taken into account; roth is after tax and pre tax is before tax. They are both retirement accounts. The difference is 401(k) is employee sponsored where as IRAs are individual accounts between you and your broker.

I assume these are 401k plans.

Pre-tax (Standard): Pay taxes on your contributions upon withdrawal. This lowers your current taxable income, which may be beneficial.

Roth: Pay taxes on your contributions now. Gets taxes out of the way (no one knows what future tax brackets may be), especially good if you start your career in a lower tax bracket. For most high-earners, a Roth 401k is usually not a good idea.

After-tax: This is a standard 401k but you can add additional money (already taxed like in a Roth) above the standard contribution limit ($22,500 for 2023 and if <50) to a max of $66k (including employer match) in 2023 if <50. However, earning are taxed, and is the only plan where this is so.

Now sure why the standard Pre-Tax and After-Tax are both offered (After-Tax is the same if you don’t contribute over $22,500 from paycheck deductions). Only thing I can think of is that the funds/investments offered are different.

General advice is to either invest in index funds (S&P 500, Total US Market, Total Foreign Market, Total World Market) or invest into Target Date Funds (you select the one with a date closest to your retirement date and it handles the allocation of investments for you and changes every year, doing more stocks at the start and more bonds towards the end). And make sure the expense ratios (fees) are low, below 1% for sure but below 0.25% even more so.

One thing not mentioned so far is that a Roth is not subject to Required Minimum Distribution) RMD when you reach mid 70's, which can jack up your taxes paid well into retirement. This is why Roth conversions are a thing.

A traditional (pre-tax) IRA means you put the money in an account before taxes are taken, and then this money is allowed to grow tax free as long as it remains in the account. When you start to pull money out the money is treated as ordinary income (it's as if you're making a salary equal to the amount you withdraw). This is best if you expect your tax burden to be lower in retirement than they are currently (generally you expect to have a lower income in retirement). What this means is that you really own about 70% or so of whatever your balance is in a traditional IRA, with the government owning 30% or so they'll collect in taxes when you start making withdrawals.

A Roth (after tax) IRA means you the money you are putting in the account has already been taxed. You've already paid taxes on the money you put in, and any increase in value will also be tax free when you withdrawal it. If you think you will make more money in retirement, or tax burdens will increase (considering the spending of the government this is probably a good bet) the the Roth IRA is for you.

These comments are all based on the assumption that the government doesn't change its mind sometime in the future, and thinks that it is unfair for you to have saved for your retirement when other people did not. Every so often (and likely to increase as the government becomes more cash strapped) you'll hear whispers of the government wanting to tap these accounts--applying means testing or some other things. I think they're safe in the mid-term future, but if things get really bad I wouldn't be surprised if the government does what governments do and steals your money.

The mentions above are about the basic rules, but there are a bunch of other ones around how and when you can withdrawals, and some income tests for individual IRAs.